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Lesson Posted on 18/08/2018 Learn Circles

Basics of Circle

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

The equation of a circle with its centre at C(x0, y0) and radius r is: (x – x0)2 + (y – y0)2 = r2 If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2. If r = 0 then the circle represents a point or a point... read more

Components of Circle

The equation of a circle with its centre at C(x0, y0) and radius r is:

(x – x0)2 + (y – y0)2 = r2   

              

If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2.   

If r = 0 then the circle represents a point or a point circle.

The equation x2 + y2 + 2gx + 2fy + c = 0 is the general equation of a circle with centre

(–g, –f) and radius √(g2+f2-c).

              

Equation of the circle with points P(x1, y1) and Q(x2, y2) as extremities of a diameter is

(x – x1) (x – x2) + (y – y1)(y – y2) = 0. 

              

For general circle, the equation of the chord is x1x + y1y + g(x1 + x) + f(y1 +y) + c = 0

 

 For circle x2 + y2 = a2, the equation of the chord is x1x + y1y = a2

 

              

 

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Answered on 05/12/2016 Learn Circles +2 Mathematics Class IX-X Tuition

Tanay Likhar

Math Mentor

So, if you draw a circle it will form a right angle triangle with hypotenuse 5 cm and base 3 cm. using Pythagoras theorem, the length will be equal to 4 cm.
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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD?

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent?

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

If a line segment joining midpoints of two chords of a circle passes through the centre of the circle,... read more
If a line segment joining midpoints of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel? read less

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

Two chords AB and AC of a circle subtends angles equal to 90 degree and 150 degree, respectively at the... read more
Two chords AB and AC of a circle subtends angles equal to 90 degree and 150 degree, respectively at the centre. Find the angle BAC, if AB and AC lie on the opposite sides of the centre? read less

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length?

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord?

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

Find the locus of centres of circles which touch two intersecting lines?

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Asked on 29/10/2016 Learn Circles +2 Mathematics Class IX-X Tuition

What is the formula for area of triangle?

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